Ab initio investigations of magnetic properties of ultrathin transition ...

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Chapter 4 Collinear magnetism of 3d-monolayers on Rh substrates 4.1 3d-Monolayers on (001) oriented substrates During the past two decades, theoretical and experimental investigations were performed to understand the magnetism of ultrathin magnetic films on (001) oriented nonmagnetic substrates. Mainly the weakly interacting coinage metals (Cu, Ag, Au) and some transition metals (TMs), e.g. Pd, have been chosen as substrate in order to minimize the interaction between monolayer and substrate[1, 2]. Cu with an experimental lattice constant of ao =3.61 ˚A turned out to be an ideal template for fcc bulk TMs, while Ag (ao =4.09 ˚A) and Au (ao =4.08 ˚A) are templates to grow the bcc metals. Employing density functional theory (DFT), some general trends were identified for 3d monolayers (ML) on these substrates: (i) The magnetic moments of the monolayers are considerably enhanced as compared to the equivalent bulk systems and (ii) similar to the bulk cases, Fe, Co, and Ni are ferromagnetic (FM) on these substrates, while V, Cr, and Mn prefer a c(2 × 2) antiferromagnetic (AFM) structure, i.e., a checkerboard arrangement of antiparallel magnetic moments[3, 5], a magnetic structure which cannot be derived from respective bulk phases. Experimentally, Ortega and Himpsel studied 3d monolayers on Ag(001) and confirmed the theoretical predictions, especially the magnetism of V on Ag(001)[6]. 4.1.1 3d monolayers on Pd, Ag and W (001) substrates: Here we discuss specific theoretical results obtained of 3d monolayer on Pd(001)[3], Ag(001)[4] and W(001)[7] substrates. We will use these results to compare them to our calculational results of for 3d monolayers on Rh(001) substrates in next section. In the 3d series the overall trend of the local moments follows Hund’s first rule as shown in figure 4.1. The largest local moment of about 4 μB was found for Mn and from Mn to Ni the magnetic moment decreases in steps of 1 μB. The latter behavior is a consequence of the strong ferromagnetism in these monolayers, because they have one spin band is fully occupied so that the density of states at Fermi level (see sec. 3.1) is small or even zero, 51
52 4 Collinear magnetism of 3d-monolayers on Rh substrates then susceptibility of such systems is thus also small or zero because the spin splitting is saturated so that an additional field cannot cause an significant additional magnetic moment[118]. The magnetic moments of Ti, V, and Cr monolayers show a pronounced dependence on the substrate: Ti is magnetic on Ag, but nonmagnetic on Pd; the magnetic moment of V is reduced by more than 1.5 μB when changing the substrate from Ag to Pd; and for Cr the magnetic moment changes, in the FM (AFM) configuration, from 3.78 (3.47) μB on Ag to 3.87 (3.46) μB on Pd. Magnetic moment [μ Β ] 5.0 4.0 3.0 2.0 1.0 0.0 Ag(001) Pd(001) Rh(111) Rh(001) AFM FM AFM 1 ML 3d on Ag(001) Ag(100) Pd(001) Pd(100) V Cr Mn Fe Co Ni Figure 4.1: Local magnetic moments of 3d monolayers on Ag(001) and Pd(001) calculated for the p(1×1) ferro- (solid symbols connected by solid line) and the c(2×2) antiferromagnetic configuration (open symbols connected by dashed line)[3, 5]. Later on, it was experimentally found that Fe has a c(2×2)-AFM ground state on W(001)[11], which was theoretically predicted[8, 9, 10]. A theoretical study to predict the magnetic ground state of 3d-transition metals on W(001) substrate followed this finding[7]. The magnetic ground state was predicted to be ferromagnetic for V, Cr and Mn while Fe, Co and Ni prefer the c(2×2)-AFM order on W(001) substrate. This trend is opposite trend from what Blügel found in the case of Ag or Pd substrate as shown in figure 4.2. The 3d monolayers on W(110)[119] show the same behavior as on noble metal substrates, this clearly gives evidence that results on W(001) are an effect of hybridization with the open (001) surface. The reason of this opposite trend can be explained as following: In case of strong overlayersubstrate hybridization, the coordination number, symmetry and interlayer distance is decisive in the determination of the magnetic properties of the system. On the other hand there is a difference between a bcc (001) substrate such as W and fcc (001) substrate as Ag. For a bcc substrate each 3d-transition metal atom has only four nearest W atoms at the interface, while the surrounding atoms in the overlayer are next nearest neighbors. In the fcc substrate each 3d-transition metal atom has eight nearest neighbors, four 3d
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Mitglied der Helmholtz-Gemeinschaft
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Forschungszentrum Jülich GmbH Inst
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Abstract In this thesis, we investi
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”A human being is part of the who
Page 13 and 14: II Contents 4.2.1 Relaxations and m
Page 15 and 16: 2 INTRODUCTION (ao =3.80 ˚A) is in
Page 17 and 18: 4 INTRODUCTION understanding of our
Page 19 and 20: 6 INTRODUCTION
Page 21 and 22: 8 1 Density functional theory (DFT)
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Page 35 and 36: 22 2 The FLAPW method Then one can
Page 37 and 38: 24 2 The FLAPW method Evac is the v
Page 39 and 40: 26 2 The FLAPW method of the operat
Page 41 and 42: 28 2 The FLAPW method a matrix expr
Page 43 and 44: 30 3 Magnetism of low dimensional s
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Page 67 and 68: 54 4 Collinear magnetism of 3d-mono
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102 5 Fe monolayers on hexagonal no
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104 6 Co MCA from monolayers to ato
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116 rather subtle. To shed more lig
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118
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120 where, the relation � i H =
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122 Figure 6.8: The real (left) and
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124 E(q) = −M 2 ( 2J2 +2J6 +cos(
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126 For a 2D hexagonal lattice, the
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128 Bibliography [12] P. Ferriani,
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130 Bibliography [39] A. Dallmeyer,
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132 Bibliography [68] J. Perdew and
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134 Bibliography [101] L. Nordströ
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136 Bibliography [130] O. Le Bacq,
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138 Bibliography [160] P. M. Marcus
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140 Bibliography [190] R. Germar, W
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Acknowledgement I don’t know how
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Schriften des Forschungszentrums J
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